Random and aperiodic quantum spin chains: A comparative study

TL;DR

This study compares the critical behavior of random and aperiodic quantum Ising chains, revealing universal and non-universal aspects of their phase transitions and differences in Griffiths singularities.

Contribution

It provides a detailed analysis of how different types of fluctuations affect the universality class of quantum spin chains, highlighting similarities and differences between random and aperiodic systems.

Findings

At criticality, both systems exhibit similar behavior due to broad energy scale distributions.

Critical exponents depend on the fluctuation exponent omega, with some universal and some distribution-dependent.

Aperiodic models lack Griffiths singularities in the off-critical region.

Abstract

According to the Harris-Luck criterion the relevance of a fluctuating interaction at the critical point is connected to the value of the fluctuation exponent omega. Here we consider different types of relevant fluctuations in the quantum Ising chain and investigate the universality class of the models. At the critical point the random and aperiodic systems behave similarly, due to the same type of extreme broad distribution of the energy scales at low energies. The critical exponents of some averaged quantities are found to be a universal function of omega, but some others do depend on other parameters of the distribution of the couplings. In the off-critical region there is an important difference between the two systems: there are no Griffiths singularities in aperiodic models.